I did this drive two weeks ago for the book tour--although I started in Erie, PA i/o Chicago. I highly recommend:
Millers Grocery, Christiana, TN (about 20 minutes south/east of Nashville)
Someone posted about this place 
here, which is how I found out about it. Made-from-scratch, old school comfort food at its finest--everything from congealed salads to chicken fried steak. The fruit tea is a must. 
They have odd, short hours, so I'd call or double-check the web site before stopping in. 
Germantown Commissary, Memphis, TN
I asked a bookstore clerk to send me to a non-chain, local-favorite BBQ place, and he directed me here. You could smell the hickory about three blocks away. There are some not-so-rave reviews on it (in a thread about a similar route south) 
here, but I really liked my pulled pork sandwich. I also had a fantastic slice of lemon icebox pie. 
Jackson, MS, as you've probably gathered by the lack of responses, is a bit of a culinary wasteland. I can recommend a great independent bookstore (Lemuria) and a place to get a decent cocktail (bar at the Edison Walthall Hotel--bartender's name is Whitey), but food was a bust.
This is probably out of the way, but 
Joe's Dreyfus Store Restaurant is, without a doubut, "worth a detour". A fine example of Cajun cuisine, and the little trek off 10 outside of Baton Rouge gives you a good look at one of the old backroads of Louisiana. 
I also have recommendations if you happen through or near Monroe, Marksville, Ferriday or Covington, Louisiana. 
Bring some good weather back.